Java实现一元线性回归

最近在写一个荧光图像分析软件，需要自己拟合方程。一元回归线公式的算法参考了《Java数值方法》，拟合度R^2（绝对系数）是自己写的，欢迎讨论。计算结果和Excel完全一致。

总共三个文件：

DataPoint.java

/*** A data point for interpolation and regression.*/public class DataPoint{ /** the x value */ public float x; /** the y value */ public float y;

/** * Constructor. * @param x the x value * @param y the y value */ public DataPoint(float x, float y) { this.x = x; this.y = y;

}}

/*** A least-squares regression line function.*/

import java.util.*;import java.math.BigDecimal;

public class RegressionLine //implements Evaluatable{ /** sum of x */ private double sumX; /** sum of y */ private double sumY; /** sum of x*x */ private double sumXX; /** sum of x*y */ private double sumXY; /** sum of y*y */ private double sumYY; /** sum of yi-y */ private double sumDeltaY; /** sum of sumDeltaY^2 */ private double sumDeltaY2; /**误差 */ private double sse; private double sst; private double E; private String[] xy ; private ArrayList listX ; private ArrayList listY ; private int XMin,XMax,YMin,YMax; /** line coefficient a0 */ private float a0; /** line coefficient a1 */ private float a1;

/** number of data points */ private int pn ; /** true if coefficients valid */ private boolean coefsValid;

/** * Constructor. */ public RegressionLine() { XMax = 0; YMax = 0; pn = 0; xy =new String[2]; listX = new ArrayList(); listY = new ArrayList(); }

/** * Constructor. * @param data the array of data points */ public RegressionLine(DataPoint data[]) { pn = 0; xy =new String[2]; listX = new ArrayList(); listY = new ArrayList(); for (int i = 0; i < data.length; ++i) { addDataPoint(data[i]); } }

/** * Return the current number of data points. * @return the count */ public int getDataPointCount() { return pn; }

/** * Return the coefficient a0. * @return the value of a0 */ public float getA0() { validateCoefficients(); return a0; }

/** * Return the coefficient a1. * @return the value of a1 */ public float getA1() { validateCoefficients(); return a1; }

/** * Return the sum of the x values. * @return the sum */ public double getSumX() { return sumX; }

/** * Return the sum of the y values. * @return the sum */ public double getSumY() { return sumY; }

/** * Return the sum of the x*x values. * @return the sum */ public double getSumXX() { return sumXX; }

/** * Return the sum of the x*y values. * @return the sum */ public double getSumXY() { return sumXY; } public double getSumYY() { return sumYY; } public int getXMin() {return XMin;}

public int getXMax() {return XMax;}

public int getYMin() {return YMin;}

public int getYMax() {return YMax;} /** * Add a new data point: Update the sums. * @param dataPoint the new data point */ public void addDataPoint(DataPoint dataPoint) { sumX += dataPoint.x; sumY += dataPoint.y; sumXX += dataPoint.x*dataPoint.x; sumXY += dataPoint.x*dataPoint.y; sumYY += dataPoint.y*dataPoint.y; if(dataPoint.x > XMax){ XMax = (int)dataPoint.x; } if(dataPoint.y > YMax){ YMax = (int)dataPoint.y; } //把每个点的具体坐标存入ArrayList中，备用 xy[0] = (int)dataPoint.x+ ""; xy[1] = (int)dataPoint.y+ ""; if(dataPoint.x!=0 && dataPoint.y != 0){ System.out.print(xy[0]+","); System.out.println(xy[1]); try{ //System.out.println("n:"+n); listX.add(pn,xy[0]); listY.add(pn,xy[1]); } catch(Exception e){ e.printStackTrace(); } /* System.out.println("N:" + n); System.out.println("ArrayList listX:"+ listX.get(n)); System.out.println("ArrayList listY:"+ listY.get(n)); */ } ++pn; coefsValid = false; }

/** * Return the value of the regression line function at x. * (Implementation of Evaluatable.) * @param x the value of x * @return the value of the function at x */ public float at(int x) { if (pn < 2) return Float.NaN;

validateCoefficients(); return a0 + a1*x; } public float at(float x) { if (pn < 2) return Float.NaN;

validateCoefficients(); return a0 + a1*x; }

/** * Reset. */ public void reset() { pn = 0; sumX = sumY = sumXX = sumXY = 0; coefsValid = false; }

/** * Validate the coefficients. * 计算方程系数 y=ax+b 中的a */ private void validateCoefficients() { if (coefsValid) return;

if (pn >= 2) { float xBar = (float) sumX/pn; float yBar = (float) sumY/pn;

a1 = (float) ((pn*sumXY – sumX*sumY) /(pn*sumXX – sumX*sumX)); a0 = (float) (yBar – a1*xBar); } else { a0 = a1 = Float.NaN; }

coefsValid = true; } /** * 返回误差 */ public double getR(){ //遍历这个list并计算分母 for(int i = 0; i < pn -1; i++) { float Yi= (float)Integer.parseInt(listY.get(i).toString()); float Y = at(Integer.parseInt(listX.get(i).toString())); float deltaY = Yi – Y; float deltaY2 = deltaY*deltaY; /* System.out.println("Yi:" + Yi); System.out.println("Y:" + Y); System.out.println("deltaY:" + deltaY); System.out.println("deltaY2:" + deltaY2); */ sumDeltaY2 += deltaY2; //System.out.println("sumDeltaY2:" + sumDeltaY2); } sst = sumYY – (sumY*sumY)/pn; //System.out.println("sst:" + sst); E =1- sumDeltaY2/sst; return round(E,4) ; } //用于实现精确的四舍五入 public double round(double v,int scale){

if(scale<0){ throw new IllegalArgumentException( "The scale must be a positive integer or zero"); } BigDecimal b = new BigDecimal(Double.toString(v)); BigDecimal one = new BigDecimal("1"); return b.divide(one,scale,BigDecimal.ROUND_HALF_UP).doubleValue();

} public float round(float v,int scale){

} }

演示程序：

LinearRegression.java

/*** Linear Regression* * Demonstrate linear regression by constructing the regression line for a set* of data points.* * require DataPoint.java,RegressionLine.java * * 为了计算对于给定数据点的最小方差回线，需要计算SumX,SumY,SumXX,SumXY; (注：SumXX = Sum (X^2))* 回归直线方程如下： f(x)=a1x+a0 * 斜率和截距的计算公式如下：* n: 数据点个数* a1=(n(SumXY)-SumX*SumY)/(n*SumXX-(SumX)^2)* a0=(SumY – SumY * a1)/n * (也可表达为a0=averageY-a1*averageX)* * 画线的原理：两点成一直线，只要能确定两个点即可 * 第一点：(0,a0) 再随意取一个x1值代入方程，取得y1，连结(0,a0)和(x1,y1)两点即可。* 为了让线穿过整个图,x1可以取横坐标的最大值Xmax，即两点为(0,a0),(Xmax,Y)。如果y=a1*Xmax+a0,y大于* 纵坐标最大值Ymax，则不用这个点。改用y取最大值Ymax，算得此时x的值，使用(X,Ymax)，即两点为(0,a0),(X,Ymax)* * 拟合度计算：(即Excel中的R^2)* *R2 = 1 – E* 误差E的计算：E = SSE/SST* SSE=sum((Yi-Y)^2) SST=sumYY – (sumY*sumY)/n;* */public class LinearRegression{ private static final int MAX_POINTS = 10; private double E;

/** * Main program. * * @param args * the array of runtime arguments */ public static void main(String args[]) { RegressionLine line = new RegressionLine();

line.addDataPoint(new DataPoint(20, 136)); line.addDataPoint(new DataPoint(40, 143)); line.addDataPoint(new DataPoint(60, 152)); line.addDataPoint(new DataPoint(80, 162)); line.addDataPoint(new DataPoint(100, 167)); printSums(line); printLine(line); }

/** * Print the computed sums. * * @param line * the regression line */ private static void printSums(RegressionLine line) { System.out.println("/n数据点个数 n = " + line.getDataPointCount()); System.out.println("/nSum x = " + line.getSumX()); System.out.println("Sum y = " + line.getSumY()); System.out.println("Sum xx = " + line.getSumXX()); System.out.println("Sum xy = " + line.getSumXY()); System.out.println("Sum yy = " + line.getSumYY()); }

/** * Print the regression line function. * * @param line * the regression line */ private static void printLine(RegressionLine line) { System.out.println("/n回归线公式: y = " + line.getA1() + "x + " + line.getA0()); System.out.println("拟合度： R^2 = " + line.getR()); } }

快乐不是因为得到的多而是因为计较的少！

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